Question

1. You are hired by the governor of New York to study whether a tax on liquor has decreased average liquor consumption in your state. You are able to obtain, for a sample of individuals selected at random, the difference in liquor consumption in ounces) for the years before and after the tax. For person i who is sampled randomly from the population, Y, denotes the change in liquor consumption. Suppose we know that the variance of the decrease in liquor consumption is 400 (0 = 400). We do not know the mean ji of the decrease in liquor consumption and we estimate it using a sample of 400 people. We estimate p using Y which is based on the sample people: y Y1 + y2 + Y3 +... Y400 100Y 400 400 (a) Suppose the liquor tax actually had no impact on consumption (n = 0), what is the probability of finding a Y of 1.5 ounces or more in your sample (Find PY < -1.5 j = 0)) (b) Suppose the average person in your sample does reduce liquor consumption by 1.5 ounces (Y = -1.5). What is the range of potential values that you are 70% confident contains ? (c) The governor feels 70% is too low a level of confidence. There is a 30% chance the population level change in liquor consumption was outside the range you specified. What is the range of potential values that you are 99% confident contains ? (d) Suppose you have a sample of 2,500 people. Your sample mean with the larger sample is slightly different, it is Y = -1. Find the probability of getting a sample mean of -1 with n=2,500, if the true i for the population is 0.